The cost of manufacturing x cases of umbrellas is C dollars (in thousands), where

Monthly production at t weeks is expected to be

I know that = 18(5000+80t)+4sqrt(5000+80t)+9

and that marginal cost or = 28+(2/x^.5)

I'm not sure how to find in order to solve the equation for t=2 in order to find how fast costs are rising per week.

Hiya Terry by the step where you list = 18(5000+80t)+4sqrt(5000+80t)+9 , you are on the right track. Since you now have C(t), you can differentiate to find without having to worry about the chain rule with other variables.